Rattle - Rear Window Shelf
 

I have a second issue with my new to me Civic. There is a rattle coming from (I think) the rear "shelf" (behind the rear seats and the rear window, where the speakers are mounted). I'm guessing I could easily fix this if I could get this shelf out but can this be done without taking the rear glass out?

The car has some warranty left. Would a dealership warranty something like this?

Thanks in advance.